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Many models have been proposed to minimize the dark matter (DM) content invarious astronomical objects at every scale in the Universe. The most widelyknown model isMOdified Newtonian Dynamics (MOND). MOND was first published byMordehai Milgromin 1983 (Milgrom, 1983; 2015; see also Banik and Zhao, 2022 fora review). A second concurrent model is modified gravity (MOG), which is acovariant scalar-tensor-vector (STVG)extension of general relativity (Moffat,2006; 2020). Other theories also exist but have notbeen broadly applied to alarge list of astronomical objects (Mannheim and Kazanas, 1989;Capozziello andDe Laurentis, 2012; O'Brien and Moss, 2015; Verlinde, 2017). A new model,called$\kappa$-model, based on very elementary phenomenological considerations, hasrecently beenproposed in the astrophysics field. This model shows that thepresence of dark matter canbe considerably minimized with regard to thedynamics of galaxies (Pascoli, 2022 a,b). The$\kappa$-model belongs to thegeneral family of theories descended from MOND. Under this familyof theories,there is no need to develop a highly uncertain dark matter sector of physicstoexplain the observations.

A comparative study of MOND and MOG theories versus the$\kappa$-model: An application to galaxy clusters